Side DF is congruent (the = and ~ symbol) to side DE
Answer:
The correct option is A) [tex]\overline{DF}\cong \overline{DE}[/tex]
Step-by-step explanation:
Consider the provided figure.
The coordinates of E is (-2,3)
The coordinates of D is (-5,1)
The coordinates of F is (-3,-2)
Now use the distance formula to find the length of line segment:
[tex]\left(x_1,\:y_1\right),\:\left(x_2,\:y_2\right):\quad \sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}[/tex]
The distance between (-2,3) and (-5,1) is:
[tex]\overline{DE}=\sqrt{\left(-5-\left(-2\right)\right)^2+\left(1-3\right)^2}=\sqrt{13}[/tex]
The distance between (-5,1) and (-3,-2) is:
[tex]\overline{DF}=\sqrt{\left(-3-\left(-5\right)\right)^2+\left(-2-1\right)^2}=\sqrt{13}[/tex]
The distance between (-3,-2) and (-2,3) is:
[tex]\overline{EF}=\sqrt{\left(-2-\left(-3\right)\right)^2+\left(3-\left(-2\right)\right)^2}=\sqrt{26}[/tex]
Hence the length of line segment DE and DF is same.
Thus the correct option is A) [tex]\overline{DF}\cong \overline{DE}[/tex]
